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2311_T2A_solutions_F11

2311_T2A_solutions_F11 - v r A MAC2311 Test 2(form A Name(0...

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Unformatted text preview: v r A MAC2311 Test 2 (form A) Name: [(0 LL 0’71; Fall, 2011 Section (circlcyours) MWF 9:00 MWF 10:00 Calculator allowed. Unless otherwise directed, show work to earn partial credit. 1. When an object is projected vertically upward from the ground, its height in feet at time I seconds is given by SQ) = 641F461? feet for 0 S t S 4. Average Velocity (seconds flee: er second [m] Liv-£4 “3,2.- V @10ch :: S , 00/ 2: filfifljéfiifl :- -=~ 32 . ore . 00/ b) Find 12(3) , the instantaneous velocity at time i: 3 , by using the limit definition of derivative to a) Complete the table by calculating average velocity over the time interval 3 S t 5 3.001. Do not round off. .. record all digits shown by your calculator’s default settings. calculate s’(3) Show all work to support your answer, and use appropriate units. 5a)? is flew-5(3) v(3):s’(3)='“32~ Ft’sec: ln-ezo Z x m 3ft!iiéle:%l§;;52w:mi§m To H2 MM w/éfijflwifilwg :2. {M wwwwwwmwr _. _ W0 h if” it? ' ’ m t” W" "' / A Yam’s Temperature (degrees Celsius) 30p 2. A cold Yam is placed in an oven preheated to 150°C . T The graph shows the Yam’s temperature over a 3-hour period. Sketch the tangent line to the graph at time I: 1 hour, and estimate it’s slope. Then fill in the blanks below to complete conceptual interpret for this slope. Edi/{maiith (hug) “Mi (11‘733 tm - a: N - 5-02, nitrate.“ aw wr“ ‘ w Conclusion: An hour after being in the oven the Yam’s temperature is increasing at an ‘I (15 inmihmflw rate of 50 ofi’flr ( average 0! instantaneous ) ( numerical answerwithappmpriateunits ) 3. The piecewise—defined f ~ graph shown is made from connecting a straight line segment and a quarter circle. Sketch f’ . Be sure your sketch uses open/solid dots as needed. If the f’ graph is asymptotic, use a dashed line to indicate the asymptote and label it with its equation. Graph of f Graph of f ' 1 3 4 5 ml m leak ‘i’W-mrcil iw (3-49 Keg? H2 5+4xwx2 , x34 4. One piece of the graph of f ={ b 4 mx+ , x > is shown. Find values form and b that make f differentiable at x = 4. Four” Kéllv) fiC’(x):ewa;x_ fézf)fiLl”Z(H)$mLi' - Ai‘" Tali; 51/0 We”, is, $0 Wig, \fiitt‘é‘féw 0w" m;+b in be. 2%)»: “tr-lo. y y mofi 6 7 m= we!“ : . -=- t W:- ‘2 , _{_ I. p) ansmwg éga'ignm‘a ) we Nafii‘ 2/3,»: 93 ii) m w L} xai Pie Pdln'i” a all x + 2.! 5. The function f(_x) = 313)(x— 2)2 = 306—2); has domain (—00,+00). 3) Calculate f ’(x) and state its domain. ’% Z'H‘v—‘I I f'(x): '3: I I 7) i c =_ 2:. —z e i}: X) 3) 50‘ ) 1 domain of f’ ("’o"; 2") U(9‘I+m) \ I '73 2. JZLK):'2(>('Z 1.: 3x ‘For‘ Xi; N 1)) Sketch enough of the f -graph to Show its true behavior at x = 2. The one—sided limits of f ’(x) as x—> 2‘ and x a}? may be useful 2— L 3? 31 i—xi E“: Ki \3/ X'Z =1 no.9 0 = '- 00 . iinjia'hii’eiy 'Si‘m? - .3 ‘ u . 2“ 6’03‘94'“ 6&5? if» Kriz lm+ 3 1,; 5 #II .- 751 1—};0 . . _5 . D 39.2 \jK—l Pct‘ose 1‘0 0 6. Consider the table describing function j and the graph of function k. I. 6. 5. 4. Graph of k Let h(x)=j(x) m3): (ii/fie ke)‘ I , Koo my} (*2: Hemmwwu iwnufimmfie m3) ‘filfiildflifigiil :2 fate :1 A 7. Choose either A. or B. but not both. Check the box for the problem you want graded. A. D The graph of f(x) =x+2cosx has an infinite number of horizontal tangents. Find the exact radian measure x-coordinatcs of these horizontal, expressing the final answer using parameter n. Be sure to state whether your 11 represents all integers, all odd integers, all even integers, etc. i \ $(K) 2:“ H2.sz Q Km’w-Zg‘mx _W ,fifiww-msur» » {c'*F¢JTa‘.Z-—ML"~“:- m WW 8. Find each derivative: fiwfi:vlmfi.'rd,qaxapffixhfi:vfi 4, fly L MWMwi‘fifitfl/WWN” >< vs o-“"” B. [:I Find the eguation of the tangent line to the graph of y : cos"I x at x = 0 . Simplification is not required, but the y—coordinate of point of tangency must be expressed in exact radian measure form. owe a?) *‘ J :a ._ 2 .. «L 3) y='(2l 1) Answe1 Q: Aim X?» x dx ~| y: “Xmfljfls a. 1+ x - ‘t “‘3' X X b) y=lr1(1+e‘”) H B (A I 1 x < E “6‘” Q? ex. ‘ m ammmzwsafiwwwfiw W 1-» Pg? area Vmwmgwwwia first Helix iii: i‘i' e.“ H ... K"- : “W gem j t 3:. er “M” “33%. g e 1+ 9. Choose either A. or B. but not both. Check the box for file problem you want graded. A A. [:1 Find an eguation for the tangent line to the graph of 3c2 + xy — y2 : 4 at the point (2,2). equation: E: “a 2x+x¢§fl+7~miy§izo at \agwwm, a *fi”2‘/“fiw RY )2 X 2 y an 3x «a. [3% B. [3 Use logarithmic differentiation to find 3% for y = x‘a’”. Express the final answer explicitly as a functlon of x. E g +6,“ K %>/ :2. R X rhea”: ' {fig ¥Ex3 _ {WK . 5;” +7, [ex , 593% 10. A movie camera is positioned 3000 feet from the base a rocket launch pad. Assume the rocket rises vertically, and it’s speed is 600 ft/sec at the moment when the rocket has risen 4000 feet. How fast is the distance between the rocket and camera increasing at this moment? Express the final answer using appropriate units. t d aux/QM, \ Q it / 4L $3 {M'V‘C‘ 739L000 / / C / W "L at? i: i 7 300024 50000 '3: C: Answer: 3: $1180 iii/age 6 e3: EC) CD c3 11. Grain is dumped from a conveyor belt at a constant rate of 40 fia/min . The grain forms a conical pile whose heighLis alwaxi twice its radius. How fast is the radius of the pile increasing when the radius is 5 feet? 1 For a cone, V = marrzh . Expr $3 the answer either in exact form or in decimal form rounded to the 3 - 3'” t . all! 2. .__ I is Qwew gate/4W.” ...
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